Reduce to lowest terms: $ \dfrac{5}{9} \div \dfrac{8}{5} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{8}{5}$ is $ \dfrac{5}{8}$ Therefore: $ \dfrac{5}{9} \div \dfrac{8}{5} = \dfrac{5}{9} \times \dfrac{5}{8} $ $ \phantom{ \dfrac{5}{9} \times \dfrac{5}{8}} = \dfrac{5 \times 5}{9 \times 8} $ $ \phantom{ \dfrac{5}{9} \times \dfrac{5}{8}} = \dfrac{25}{72} $